*4.1. Identification of Optimization Directions in PLES*

The ternary phase diagram can visually represent the ratio of PLES in any region, where the endpoints of the triangle indicate a production/living/ecological space ratio of 100% (Figure 7). According to the threshold value of the impact of PLES on the ES supply and demand imbalance, when the ratio of living space is less than 15.68%, the ratio of production space is between 18.2 and 62.83%, and the ratio of ecological space is between 29.79% and 88.61%, while the ES involved in this study are all in surplus. Accordingly, an ideal area, i.e., an area that does not need to be optimized, can be obtained. When the projection of an area falls within the ideal area, it means that this type of area does not need to be optimized, while the rest of the area needs to be optimized to varying degrees, depending on its location. The PLES of a region can be adjusted according to the range in the diagram where the ratio of PLES of any region falls. The greater the distance from the ideal area, the greater the area of change required in the land use pattern of the region.

The size of the ideal area is usually related to the ES selected. The more ES selected, the smaller the ideal area will be in response, meaning that more area will need to be adjusted. The ES can therefore be adjusted in the actual management process to suit the needs of the policymaker accordingly.

**Figure 7.** Ternary phase diagram of production-living-ecological space.

#### *4.2. Optimization Measures and Policy Recommendations at Different Scales*

The distribution of PLES was highly spatially heterogeneous, which led to a spatial mismatch in ES. Therefore, the PLES optimization should be coupled with optimization measures at different scales to determine the best measures for ecosystem service manage-

ment. In this study, the ratios of PLES at different scales were counted, and this was used to obtain optimization measures at multiple scales (Figure 8).

**Figure 8.** Optimization of production-living-ecological space on multiple scales ((**a**). the 40 × 40 km grid scale; (**b**). the 20 × 20 km grid scale; (**c**). the primary catchment scale; (**d**). the secondary catchment scale; (**e**). the city scale; (**f**). the county scale. TheIto XI corresponds to Figure 7 numbering).

At the grid-scale, there was too much ecological space and not enough production space in the north-western part of the study area, and there is a need for conversion of ecological to production space, such as converting unused land in the area to industrial land. The central part of the study area had too much production space and not enough ecological space, so there is a need to convert the production land in the area to ecological land, such as implementing a system of returning farmland to forest or converting farmland unsuitable for cultivation to forest land. The eastern part of the study area, i.e., the lower reaches of the Yellow River Basin, was mainly characterized by an excess of living space and production space and a shortage of ecological space, so it is necessary to shift the production/living space towards ecological space, increasing the ratio of ecological space and reducing living space. For example, increase the woodland and grassland and reduce the rate of urbanization development. At the primary watershed scale, most of the Midwest was in the ideal mode of PLES, i.e., it did not need to be optimized. There was an excess of productive space in the eastern region and an excess of living space in the coastal region. At the secondary watershed scale, the central and western regions of the study area had

more watersheds that need to be optimized, and they behaved in much the same way spatially as at the grid-scale. At the city scale, Erdos had too much ecological space and not enough production space, while Weinan had too much production space. At the county scale, some counties in the central region showed a shortage of production space, while others showed an excess of production space and a shortage of ecological space, implying that production space was not evenly distributed at the county scale in the region.

In conclusion, as the statistical scale increases, there is a general trend towards fewer areas in need of spatial optimization. The main problem in the north-western part of the study area was that there was too much ecological space and not enough production space. Therefore, it is necessary to increase the area of production land in the region, and as the region is also the main area of the Loess Plateau and undertakes important functions of soil and water conservation, the area of regional terraces and industrial land can be increased appropriately. The central part of the study area showed an uneven distribution of production space and a lack of ecological space, so it is necessary to adjust the distribution of production space at several scales to ensure that it is in a reasonable range, while the ratio of ecological land, such as woodland and grassland, can be increased appropriately. The eastern part of the study area had a large ratio of production space and living space area and too little ecological space. Therefore, it is necessary to reduce and harmonize production and living space, while increasing the right amount of ecological space, such as green space and woodland. Here, the direction of the PLES adjustment is mainly explained, which in practice it can be quantified according to the difference between the PLES ratio of a region and the ideal region.
